MCR3U1
Page |1
Art Meets Math – Drawing with Graphs
Group: _____ Members:_______________________________________________________________
___________________________________________________________________________________
Math class isn’t just about math, and graphs can be used for non-mathematical purposes.
For this activity, I want you to create a drawing with the graphs of algebraic expressions. You have
learned about some of them in detail, and you will need to explore properties of other expressions during
this activity. I have provided a list of algebraic expressions and their corresponding general
transformation equations. You can choose at least 4 different algebraic expressions, and you need to
apply some transformations to each of them. You will also need to produce a written list of equations
and their domains that correspond to the graphs you have drawn. A very simple example of what is
expected of you is attached to this activity.
I have attached a few images that you can choose to recreate with these algebraic expressions. You can
pick and choose part of the image to draw then hand draw the rest. If you want to create an original
image, you can sketch it out and get it approved by either Mr. Chan or myself.
You can use desmos.com as a tool to help you visualize the graphs of different algebraic expressions
and the entirety of your image. You can print off the drawing from desmos then outline the drawing with
marker. However, I want you to hand draw the final product on graphing paper. You are welcome to
colour the drawing and make it look pretty.
You will be working in groups of 4-5 people. A group leader will be chosen, and the leader is
responsible for keeping the group on task. Each group must distribute the workload evenly and make
sure that everyone is involved in the decision making process.
Checklist to Success
□ We worked as a team.
□ We have used at least 4 DIFFERENT algebraic expressions. List them.
1. ________________________________
2. ________________________________
3. ________________________________
4. ________________________________
□ We have applied transformation to all the expressions.
□ List of equations and their domains.
□ All graphs and corresponding equations are labeled.
□ The drawing looks like the original image.
MCR3U1
Page |2
List of algebraic expressions, and their general transformation equation:
Linear:
𝒚=𝒙
y = mx + b
Even:
𝒚 = 𝒙𝟐 , 𝒚 = 𝒙𝟒 , etc.
𝑦 = 𝑎[𝑘(𝑥 − 𝑑)2 ] + 𝑐, 𝑦 = 𝑎[𝑘(𝑥 − 𝑑)4 ] + 𝑐
Odd:
𝒚 = 𝒙𝟑 , 𝒚 = 𝒙𝟓 , etc.
𝑦 = 𝑎[𝑘(𝑥 − 𝑑)3 ] + 𝑐, 𝑦 = 𝑎[𝑘(𝑥 − 𝑑)5 ] + 𝑐
Horizontal Line:
𝒚=𝒂
Change 𝑎
Vertical Line:
𝒙=𝒂
Change 𝑎
Square Root Function:
𝒚 = √𝒙
𝑦 = 𝑎√k(x − d) + 𝑐
Exponential:
𝒚 = 𝒃𝒙
𝑦 = 𝑎(𝑏 𝑘(𝑥−𝑑) ) + 𝑐
Absolute Value Function:
𝒚 = |𝒙|
𝑦 = 𝑎 |𝑘(𝑥 − 𝑑)| + 𝑐
Inverse Functions:
𝒚𝟐 = 𝒙
𝑎(𝑦 − 𝑏)2 = 𝑘(𝑥 − 𝑑)
Sine Function:
𝒚 = 𝒔𝒊𝒏𝒙
𝑌 = 𝑎 𝑠𝑖𝑛[𝑘(𝑥 − 𝑑)] + 𝑐
Equation of a Circle:
𝒙 𝟐 + 𝒚𝟐 = 𝒓 𝟐
𝑝(𝑥 − 𝑎)2 + 𝑞(𝑦 − 𝑏)2 = 𝑟 2
Centre of the circle will be translated from the origin (0, 0) to (𝑎, 𝑏).
𝑝 and 𝑞 stretches the circle into oval shaped.
Play around with equations on desmos.com to see the transformations look like for each expression.
MCR3U1
Sample Work – The Sun
Page |3
MCR3U1
Sample Work – Girl
Original Image
Page |4
MCR3U1
Desmos.com
Page |5
MCR3U1
Final Product
***the list of equations on the side on desmos.com will also be printed.
Page |6
MCR3U1
Image 1
Page |7
MCR3U1
Image 2
Page |8
MCR3U1
Image 3
Page |9
MCR3U1
Image 4
P a g e | 10
MCR3U1
Image 5
P a g e | 11
MCR3U1
RUBRIC FOR
P a g e | 12
Art Meets Math – Drawing with Graphs
Group: ______________
Names: ________________________________________________
_______________________________________________________
Total
_____
100
Categories
Level 0
Level 1
Level 2
Level 3
Level 4
Knowledge
&
Understanding
Did not use
any of the
provided
algebraic
expressions.
Used 1
algebraic
expressions
with
transformations
applied it.
Used 3 different
algebraic
expressions with
transformations
applied to each
one.
Used 4 different
algebraic
expressions with
transformations
applied to each
one.
No equations
and domains
match up to
their
corresponding
graphs.
Most of the
listed equations
and domains do
not match up to
their
corresponding
graphs.
Used 2
different
algebraic
expressions
with
transformations
applied to each
one.
Some listed
equations and
domains match
up to their
corresponding
graphs.
Most listed
equations and
domains match
up to their
corresponding
graphs.
All listed
equations and
domains match
up to their
corresponding
graphs.
Equations and
their
corresponding
graphs are not
labeled.
Most listed
equations and
their
corresponding
graphs are not
labeled clearly
or easily
identifiable.
Some listed
equations and
their
corresponding
graphs are
labeled clearly
and easily
identifiable.
Most listed
equations and
their
corresponding
graphs are
labeled clearly
and easily
identifiable.
All listed
equations and
their
corresponding
graphs are
labeled clearly
and easily
identifiable.
Group did not
work
together.
Group
demonstrated
limited
teamwork
skills.
The graphed
drawing mostly
does not
resemble the
original image.
Group
demonstrated
some teamwork
skills.
Group
demonstrated
good teamwork
skills.
Group
demonstrated
exceptional
teamwork skills.
The graphed
drawing
resembles the
original image
to a degree.
The graphed
drawing
resembles the
original image.
The graphed
drawing highly
resembles the
original image.
25%
Application
25%
Communication
5%
5%
Thinking
&
Inquiry
40%
BONUS
5%
The graphed
drawing does
not resemble
the original
image.
The image created is original.